Zines had their heyday before the easy access to the internet, but many survive today. Some of the longest running zines are MaximumRocknroll, Cometbus,BenisDead,Guttersnipe. After a few years of what looked like potential zine-extinction, some very good ones (in some form or another), have been creeping onto the internet. One particularly hard reading one is the crash site, which you can get to from www.blindwino.com.
Zines are basically broken into a few simple categories: 1. Music zines (probable the first, as "zines" comes form "fan-zines". 2. Personal zines. These are my favorite, Cometbus is a good example of this. 3. special interest zines, skate zines, locale-specific zines etc.
There are many more, but one of the most beautiful things about zines is that hardly anyone has figured out how to make any money off them. If you are in Portland, visit Reading Frenzy, in Seattle, HypnoVideo.